Abelian variety isogeny class 2.193.abw_bkq over $\F_{193}$

• Label: 2.193.abw_bkq
• Base field: $\F_{193}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{193}$
Dimension:	$2$
L-polynomial:	$1 - 48 x + 952 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:	$\pm0.0675123601384$, $\pm0.230069799779$
Angle rank:	$2$ (numerical)
Number field:	4.0.2054400.4
Galois group:	$D_{4}$
Jacobians:	$60$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28890$	$1372679460$	$51673224895290$	$1925154747813891600$	$71709016301977158272250$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$146$	$36850$	$7187762$	$1387510918$	$267785600306$	$51682541600050$	$9974730240873362$	$1925122950833556478$	$371548729888542460946$	$71708904873245099619250$

Jacobians and polarizations

This isogeny class contains the Jacobians of 60 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=165x^6+131x^5+171x^4+106x^3+115x^2+169x+30$
• $y^2=69x^6+78x^5+190x^4+148x^3+167x^2+152x$
• $y^2=70x^6+61x^5+11x^4+125x^3+50x^2+109x+141$
• $y^2=191x^6+38x^5+145x^4+166x^3+60x^2+169x+11$
• $y^2=154x^6+43x^5+35x^4+5x^3+131x^2+87x+144$
• $y^2=106x^6+51x^5+75x^4+58x^3+48x^2+73x+47$
• $y^2=153x^6+178x^5+80x^4+56x^3+67x^2+177x+152$
• $y^2=90x^6+73x^5+132x^4+138x^3+66x^2+116x+130$
• $y^2=158x^6+126x^5+63x^4+60x^3+139x^2+161x+145$
• $y^2=74x^6+64x^5+153x^4+187x^3+102x^2+122x+174$
• $y^2=52x^6+106x^5+137x^4+160x^3+161x^2+39x+110$
• $y^2=188x^6+46x^5+20x^4+171x^3+37x^2+139x+30$
• $y^2=47x^6+170x^5+143x^4+33x^3+133x^2+31x+44$
• $y^2=149x^6+57x^5+117x^4+42x^3+158x^2+x+38$
• $y^2=147x^6+59x^5+25x^4+80x^3+178x^2+53x+76$
• $y^2=47x^6+155x^5+99x^4+161x^3+83x^2+171x+86$
• $y^2=7x^6+127x^5+126x^4+53x^3+159x^2+21x+26$
• $y^2=64x^6+181x^5+179x^4+51x^3+180x^2+89x+102$
• $y^2=37x^6+56x^5+89x^4+74x^3+121x^2+117x+105$
• $y^2=119x^6+147x^5+12x^4+135x^3+59x^2+58x+123$
• and

• $y^2=121x^6+66x^5+170x^4+85x^3+21x^2+103x+117$
• $y^2=182x^6+103x^5+188x^4+184x^3+181x^2+131x+173$
• $y^2=135x^6+52x^5+37x^4+6x^3+164x^2+182x+164$
• $y^2=120x^6+6x^5+92x^4+39x^3+130x^2+87x+116$
• $y^2=158x^6+27x^5+28x^4+18x^3+152x^2+136x+82$
• $y^2=174x^6+178x^5+24x^4+89x^3+58x^2+156x+73$
• $y^2=154x^6+154x^5+84x^4+48x^3+164x^2+33x+113$
• $y^2=45x^6+161x^5+5x^4+54x^3+17x^2+104x+159$
• $y^2=93x^6+120x^5+188x^4+101x^3+97x^2+5x+36$
• $y^2=163x^6+91x^5+56x^4+39x^3+156x^2+113x+163$
• $y^2=183x^6+132x^5+106x^4+30x^3+150x^2+175x+4$
• $y^2=123x^6+68x^5+17x^4+76x^3+120x^2+42x+186$
• $y^2=167x^6+169x^5+146x^4+30x^3+41x^2+162x+51$
• $y^2=108x^6+61x^5+74x^4+160x^3+69x^2+147x+43$
• $y^2=11x^6+137x^5+71x^4+131x^3+68x^2+23x+4$
• $y^2=124x^6+145x^5+129x^4+27x^3+141x^2+66x+115$
• $y^2=159x^6+99x^5+29x^4+91x^3+87x^2+101x+11$
• $y^2=162x^6+2x^5+173x^4+8x^3+37x^2+14x+179$
• $y^2=178x^6+59x^5+151x^4+118x^3+76x^2+104x+177$
• $y^2=51x^6+41x^5+82x^4+44x^3+73x^2+22x+38$
• $y^2=174x^6+177x^5+18x^4+13x^3+111x^2+70x+122$
• $y^2=38x^6+173x^5+48x^4+128x^3+98x^2+160x+138$
• $y^2=101x^6+40x^5+173x^4+137x^3+92x^2+188x+132$
• $y^2=47x^6+104x^5+126x^4+31x^3+25x^2+183x+140$
• $y^2=104x^6+103x^5+8x^3+191x^2+164x+182$
• $y^2=19x^6+12x^5+9x^4+187x^3+143x^2+155x+157$
• $y^2=136x^6+4x^5+101x^4+166x^3+101x^2+51x+175$
• $y^2=20x^6+79x^5+131x^4+114x^3+150x^2+151x+105$
• $y^2=82x^6+12x^5+34x^4+140x^3+184x^2+10x+93$
• $y^2=154x^6+98x^5+87x^4+10x^3+68x^2+43x+110$
• $y^2=111x^6+104x^5+132x^4+133x^3+192x^2+124x+70$
• $y^2=18x^6+148x^5+44x^4+54x^3+134x^2+190x+51$
• $y^2=189x^6+47x^5+180x^4+177x^3+112x^2+170x+185$
• $y^2=166x^6+94x^5+42x^4+32x^3+91x^2+126x+28$
• $y^2=111x^6+116x^5+6x^4+56x^3+175x^2+37x+142$
• $y^2=171x^6+x^5+76x^4+105x^3+76x^2+100x+28$
• $y^2=113x^6+159x^5+43x^4+157x^3+181x^2+28x+109$
• $y^2=77x^6+139x^5+67x^4+27x^3+118x^2+150x+159$
• $y^2=147x^6+134x^5+11x^4+66x^3+145x^2+95x+48$
• $y^2=117x^5+182x^4+13x^3+51x^2+114x+78$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{193}$.

Endomorphism algebra over $\F_{193}$

The endomorphism algebra of this simple isogeny class is 4.0.2054400.4.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

Twist	Extension degree	Common base change
2.193.bw_bkq	$2$	(not in LMFDB)